Abstraction of continuous dynamical systems utilizing lyapunov functions

Christoffer Sloth*, Rafael Wisniewski

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

Abstract

This paper considers the development of a method for abstracting continuous dynamical systems by timed automata. The method is based on partitioning the state space of dynamical systems with invariant sets, which form cells representing locations of the timed automata. To enable verification of the dynamical system based on the abstraction, conditions for obtaining sound, complete, and refinable abstractions are set up. It is proposed to partition the state space utilizing sub-level sets of Lyapunov functions, since they are positive invariant sets. The existence of sound abstractions for Morse-Smale systems and complete and refinable abstractions for linear systems are shown.

Original languageEnglish
Title of host publication2010 49th IEEE Conference on Decision and Control, CDC 2010
Number of pages6
Publication date2010
Pages3760-3765
Article number5717270
ISBN (Print)9781424477456
DOIs
Publication statusPublished - 2010
Event2010 49th IEEE Conference on Decision and Control, CDC 2010 - Atlanta, GA, United States
Duration: 15. Dec 201017. Dec 2010

Conference

Conference2010 49th IEEE Conference on Decision and Control, CDC 2010
Country/TerritoryUnited States
CityAtlanta, GA
Period15/12/201017/12/2010

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